**linear_algebra**,
MATLAB codes which
carry out various linear algebra operations for matrices
stored in a variety of formats.

The formats include many defined by the LINPACK and LAPACK packages and various sparse formats.

For a given matrix format, the operations supplied may include

- Conversion to or from general rectangular format (GE).
- Determinant.
- Inverse.
- Matrix-matrix multiplication.
- Matrix-vector multiplication.
- Solution of linear systems by Conjugate Gradient (CG) method.
- Solution of linear systems by Gauss elimination.
- Transpose.

r83, a MATLAB code which contains linear algebra routines for r83 matrices (real, 64 bit, tridiagonal 3xn format).

r83_np, a MATLAB code which contains linear algebra routines for r83_np matrices (real, 64 bit, tridiagonal 3xn format, nonpivoting factorization).

r83p, a MATLAB code which contains linear algebra routines for r83p matrices (real, 64 bit, tridiagonal periodic format).

r83s, a MATLAB code which contains linear algebra routines for r83s matrices (real, 64 bit, tridiagonal scalar format).

r83t, a MATLAB code which contains linear algebra routines for r83t matrices (real, 64 bit, tridiagonal mx3 format).

r83v, a MATLAB code which contains linear algebra routines for r83v matrices (real, 64 bit, tridiagonal three vector format).

r85, a MATLAB code which contains linear algebra routines for r85 matrices (real, 64 bit, pentadiagonal format).

r8bb, a MATLAB code which contains linear algebra routines for r8bb matrices (real, 64 bit, border banded format).

r8blt, a MATLAB code which contains linear algebra routines for r8blt matrices (real, 64 bit, band lower triangular format).

r8bto, a MATLAB code which contains linear algebra routines for r8bto matrices (real, 64 bit, block toeplitz format).

r8but, a MATLAB code which contains linear algebra routines for r8but matrices (real, 64 bit, band upper triangular format).

r8cb, a MATLAB code which contains linear algebra routines for r8cb matrices (real, 64 bit, compressed band format).

r8cbb, a MATLAB code which contains linear algebra routines for r8cbb matrices (real, 64 bit, compressed border banded format).

r8ccs, a MATLAB code which contains linear algebra routines for r8ccs matrices (real, 64 bit, compressed column storage (colptr,row,value) format).

r8ci, a MATLAB code which contains linear algebra routines for r8ci matrices (real, 64 bit, circulant format).

r8col, a MATLAB code which contains utility routines for r8col's, that is, real mxn arrays, considered as n column vectors, each of length m. the data may be thought of as a matrix of multiple columns, and many operations will be carried out columnwise.

r8crs, a MATLAB code which contains linear algebra routines for r8crs matrices (real, 64 bit, compressed row storage (crs) format).

r8gb, a MATLAB code which contains linear algebra routines for r8gb matrices (real, 64 bit, general banded format).

r8gd, a MATLAB code which contains linear algebra routines for r8gd matrices (real, 64 bit, general diagonal format).

r8ge, a MATLAB code which contains linear algebra routines for r8ge matrices (real, 64 bit, general format).

r8ge_np, a MATLAB code which contains nonpivoting linear algebra routines for r8ge matrices (real, 64 bit, general nonpivoting format).

r8lt, a MATLAB code which contains linear algebra routines for r8ut matrices (real, 64 bit, lower triangular format).

r8ltt, a MATLAB code which contains linear algebra routines for r8ltt matrices (real, 64 bit, lower triangular toeplitz format).

r8ncf, a MATLAB code which contains linear algebra routines for r8ncf matrices (real, 64 bit, nonsymmetric coordinate format).

r8pbl, a MATLAB code which contains linear algebra routines for r8pbl matrices (real, 64 bit, positive definite symmetric band lower format).

r8pbu, a MATLAB code which contains linear algebra routines for r8pbu matrices (real, 64 bit, positive definite symmetric band upper format).

r8po, a MATLAB code which contains linear algebra routines for r8po matrices (real, 64 bit, positive definite symmetric format).

r8pp, a MATLAB code which contains linear algebra routines for r8pp matrices (real, 64 bit, positive definite symmetric packed format).

r8ri, a MATLAB code which contains linear algebra routines for r8ri matrices (real, 64 bit, row indexed format).

r8row, a MATLAB code which contains utility routines for r8row's, that is, real mxn arrays, considered as m row vectors, each of length n. the data may be thought of as a matrix of multiple rows, and many operations will be carried out rowwise.

r8s3, a MATLAB code which contains linear algebra routines for r8s3 matrices (real, 64 bit, slap triad (i,j,aij) format).

r8sd, a MATLAB code which contains linear algebra routines for r8sd matrices (real, 64 bit, symmetric diagonal format).

r8sm, a MATLAB code which contains linear algebra routines for r8sm (sherman-morrison) matrices (real, 64 bit, a-u*v' format).

r8sp, a MATLAB code which contains linear algebra routines for r8sp matrices (real, 64 bit, slap triad (i,j,aij) format).

r8sto, a MATLAB code which contains linear algebra routines for r8sto matrices (real, 64 bit, symmetric toeplitz n format).

r8to, a MATLAB code which contains linear algebra routines for r8to matrices (real, 64 bit, toeplitz 2*n-1 format).

r8ut, a MATLAB code which contains linear algebra routines for r8ut matrices (real, 64 bit, upper triangular format).

r8utp, a MATLAB code which carries out linear algebra operations on R8UTP matrices, real 64 bit, Upper Triangular Packed format.

r8utt, a MATLAB code which contains linear algebra routines for r8utt matrices (real, 64 bit, upper triangular toeplitz format).

r8vm, a MATLAB code which contains linear algebra routines for r8vm matrices (real, 64 bit, vandermonde format).